PX2657.5 Thermal Physics II
Introductory description
Any macroscopic object we meet contains a large number of particles, each of which moves according to the laws of mechanics (which can be classical or quantum). Yet we can often ignore the details of this microscopic motion and use a few average quantities such as temperature and pressure to describe and predict the behaviour of the object. Why we can do this, when we can do this and how to do it are the subject of this module.
The most important idea in the field is due to Boltzmann, who identified the connection between entropy and disorder. The empirical laws of thermodynamics required the existence of entropy, but there was no microscopic definition for it. The module shows how the structure of equilibrium thermodynamics follows from Boltzmann's definition of the entropy and shows how, in principle, any observable equilibrium quantity can be computed. This microscopic theory (now called statistical mechanics) provides the basis for predicting and explaining all thermodynamic properties of matter.
Module aims
The module introduces statistical mechanics and its central role in physics. It should give you an appreciation of Boltzmann's insights into the nature and role of entropy. You will see many of the ideas introduced here used in the description of the properties of matter in solid state, nuclear and astrophysics modules in the third and fourth years.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
 Introduction to Statistical Mechanics: Systems and states: microstates. Fundamental assumptions of stat. mech.
 Equilibrium State: Definition of entropy for closed system in equilibrium. Maximization of entropy of a closed system in equilibrium. Fluctuations and Large Systems
 Boltzmann distribution and Lagrange multipliers: Partition function, Z. Evaluation of Z for a spinhalf system in a magnetic field and harmonic oscillator and system with degeneracy. Relationship of Z to thermodynamic quantities E, S and F=ETS. Minimization of F in equilibrium for systems at fixed T and V. Microscopic basis for thermodynamics and relation to statistical mechanics.
 Classical Thermodynamics of Gases: Thermal equilibrium, quasistatic and reversible changes. Statistical Mechanics of Classical Gases. Thermodynamic potentials G and H. The ideal gas law, the Gibbs paradox.
 GrandCanonical ensembles: system not closed (possibility of particle exchange between systems). Bose Einstein and Fermi Dirac distribution functions. Density of states. Chemical potential. Fermi energy. Relevance of FermiDirac and BoseEinstein to matter. Phonons: Einstein model, Debye model and dispersive phonons, role of elastic modulus, phonon heat capacity, thermal expansion. Thermal properties of the free Fermi gas.
Learning outcomes
By the end of the module, students should be able to:
 Give the definitions of thermal equilibrium, the ergodic hypothesis and the various ensembles
 Explain importance of the partition function and calculate thermodynamic averages from it (this includes the FermiDirac and BoseEinstein distributions)
 Discuss the structure of statistical mechanics and explain its relation to classical thermodynamics
 Explain the notion of degeneracy and the density of states.
Indicative reading list
Concepts in Thermal Physics by S. J. Blundell and K. M. Blundell (OUP, 2010).
Further reading: Statistical mechanics: a survival guide by A. M. Glazer and J. S. Wark (OUP, 2001);
Statistical Physics by A. M. Guenault (Springer, 2007).
View reading list on Talis Aspire
Subject specific skills
Knowledge of mathematics and physics. Skills in modelling, reasoning, thinking.
Transferable skills
Analytical, communication, problemsolving, selfstudy
Study time
Type  Required 

Lectures  20 sessions of 1 hour (27%) 
Other activity  5 hours (7%) 
Private study  50 hours (67%) 
Total  75 hours 
Private study description
Working through lecture notes, solving problems, wider reading, discussing with others taking the module, revising for exam, practising on past exam papers
Other activity description
4 problem classes
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D1
Weighting  Study time  

Assessed Problems  15%  
Assessed work as specified by department 

2 hour online examination (Summer)  85%  
Answer 2 questions

Feedback on assessment
Personal tutor, group feedback
Courses
This module is Core for:
 Year 2 of UPXAFG33 Undergraduate Mathematics and Physics (BSc MMathPhys)
 Year 2 of UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 2 of UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 2 of UPXAF304 Undergraduate Physics (BSc MPhys)
 Year 2 of UPXAF300 Undergraduate Physics (BSc)
 Year 2 of UPXAF303 Undergraduate Physics (MPhys)
 Year 2 of UPXAF3N1 Undergraduate Physics and Business Studies
 Year 2 of UPXAF3N2 Undergraduate Physics with Business Studies